dburn

I am not sure what Hannie would have to say about this - it is not the kind of reasoning that gets mathematicians a bad name, but it is deeply flawed reasoning nonetheless. To see this, imagine that you have this suit: AQ987 J10653 I will make you this solemn assurance: the suit is not divided 3-0 (nor 0-3). You lead the jack, and West plays the two. You... well, what do you do? If you are ASkolnick, you might argue that once West has played the two, there are only two possible cases: West began with 42 and you should play for the drop; or West began with K2 and you should finesse. Since both cases are equally likely a priori, you face a guess at this point. You don't, of course, since from 42 West might have played the four, whereas from K2 he had to play the two. The same sort of reasoning applies to the As, Bs and Cs in ASkolnick's post - if East plays the three and the four (in either order) to consecutive tricks, one assumes that he had to do this from 43 doubleton, rather than that he chose to do it from 543 trebleton. Since Hannie will by now be wondering what happened to the poetry, I offer: There once was a fellow called Bayes Who led us all into a maze. But once we learn rules Are not masters but tools, We'll quickly emerge from the haze.

No great matter, except that you need to win the first heart with the queen in dummy, then proceed as I have indicated.

Since South appears to have bid a three-card spade suit, his most likely distribution is 3=4=3=3. Since North raised him, he is likely to be above minimum for his double and therefore to have the aces of diamonds and spades in a classic 4=1=4=4 shape. In that case, the line suggested by awm will fail whereas this will succeed: win the lead as cheaply as possible and play a spade (you can cash one or two clubs if you like, but on no account must you ruff a club before playing a spade). North wins and plays a club (he must, to avoid immediate material loss). Cash the top clubs, ruff a club in dummy, ruff a spade and play a club. North wins and exits with a spade (either the queen or a low one to South's queen). Ruff, exit with a diamond, and wait to make three more trump tricks. Of course, this line will fail if North began with a doubleton heart. But the bidding strongly suggests otherwise.

dburn has been reading foo's "mathematics" with much amusement - he was unaware of the existence of this thread until Frances referred to it in another thread, and too lazy to search for it until it appeared on the first page of threads in this forum. He has little to add to the excellent analyses by Stephen Tu, Jlall and others. He would make this general observation. The Principle of Restricted Choice may be summarised in a few simple words: always assume that a player has done something because he had to, not because he chose to. In the simple case of AK10xx xxxx one assumes when an honour drops to the right of the ace-king (from South's viewpoint) that it was played from necessity (because it was a singleton) rather than from choice (because it was selected from two honours doubleton). Thus, one finesses on the second round. In this case of AKQ9xx xx when an honour appears to the right of the ace-king-queen, one again assumes that it was played from necessity rather than from choice. But the positions are different because in the second case, LHO "must" play an honour from J10x in order to create a chance to take a trick in the suit. Thus, one plays for the drop because the holdings from which an honour "must" be played are J10x, J10 and singleton honour. Obviously, the a priori probability of J10x and J10 combined divided by two (because either honour will be played half the time) exceeds the probability of a singleton honour. The same sort of reasoning applies to this case: AK103 Q872 The ace is cashed and the nine appears to the left of the ace. If this is a singleton nine one must cash the king next; if from J9xx one must play to the queen. But the nine "must" be played from J9xx in order to create the possibility of taking a trick in the suit, and because the a priori probability of J9xx is three times the probability of singleton nine, one plays to the queen. dburn awaits with interest the view of foo on Q432 AJ85 When a small card is led to the jack, the nine appears from LHO. What should one do on the second round to avoid losing a trick in the suit?

I don't think its close at all. Nothing about this auction (as given, although 4♦ could be a super-accept of spades it is not indicated as being such) gives the leader any indication that declarer has a good spade holding. Assuming West is this good, he will not be leading the J from Jx, nor will he be leading the stiff J as it is too likely to blow a trick in the trump suit. Play for the drop. Technically, the lead of the jack can never actually blow a trick in the trump suit - all it can do is save declarer a guess if she is missing the king and the jack. Some of the time this will not matter if declarer has only a nine-card fit, but it will always be fatal if declarer has a ten-card fit (since then she would lay down the ace if left to her own devices). If for example trumps are as in the example above, declarer might run the queen anyway (this is exactly as good as cashing the ace for the purposes of avoiding a loser). If trumps are slightly weaker, Q9832 facing A764, leading the jack will "blow a trick" in the sense that declarer would otherwise play ace and another. If you believe that West would take these factors into account and, for those and other reasons, lead the jack from QJ twice as often (or more) as he would lead it from the singleton jack, you should play for the drop. If not, you should follow your normal line. From the description Frances gives of this West I cannot tell in what category I would place him.

As a matter of psychology, I prefer not to go down by following a line different from the one I would have followed left to my own devices. If I finesse and that's wrong, team-mates will jeer rather less loudly than if I play for the drop and that's wrong.

If you are playing to make, is that good enough? I mean, WEST will ruff third heart and get a trump promotion for his partner, for down one (2C, 1S loser). As unlikely as it seems, you need to play for hearts to be 3-3, win ACE, ruff heart. Club ACE, Diamond to ACE, Club king. Yeah you're right. I overlooked that I already ruffed a ♠. So playing for hearts to be 3-3 is obviously what you need to do. No, it isn't. If West is 5=2=3-3 and East 5=4=2=2, you need to finesse in hearts. Mind you, that doesn't give the opponents much for their bidding - but it is almost inconceivable that West would have shifted to a heart from three to the jack.

Without going too deeply into this, it seems to me that if West is 3=6=3=1 with the eight of spades, he needs the king-queen of diamonds for me to succeed. Then, I had better win the club with the ace and play a heart, intending to run it if not covered. If it is covered, I will ruff and play a diamond to the jack. The reason I need West to have both diamond honours on this line is that if East began with four to an honour, he can in theory defeat me by playing that honour on the first round. Since he is not very likely to do this, and since the line works against West distributions such as 2=6=4=1, I will start this way and see what turns up.

Well, at least neither you nor I fell into the trap of attempting to cash two rounds of hearts before drawing trumps. But this West must have a fairly low opinion of our bidding to lead a singleton against a slam holding an ace himself. It was important not to allow him to persist in his error by going down.

This is how I started. RHO pitches 2 more ♦'s on the trump. When you play a heart up. LHO ditches a diamond and sloughs another diamond when you ruff a heart to hand. It doesn't make sense to me to play RHO for the ♠A stiff. This means LHO passed over 1♣ with ♠QTxxxx and a singleton. Perhaps this is possible because evidently these opponents are gun-shy about bidding since they couldn't crawl past the 2 level with their 10 diamonds at green, so perhaps this is possible. Anyway, when you play a spade up, LHO flies with the Ace and plays a diamond. It may not make sense to you to play RHO for the singleton ♠A, but if he does not have it, then West has failed to raise 2♦ to 3♦ with ♠A, a singleton heart, and four-card (at least) diamond support. To me, that is at least as remarkable as the seeming impossibility (to you) that someone would fail to overcall on a two count. Still, I would not have been confident enough of my analysis to lead a low spade from dummy at trick six. Like you, I would have crossed to hand with a heart ruff and led a low spade. West, who does not know that he could have beaten me by playing any spade apart from the ace (I would have ducked the queen) has played the ace, and now I need to consider whether his actions are more consistent with ♠Axxxx ♥x ♦xxxx ♣xxx or with the same hand with the queen of spades instead of a low card. Since it is hard to draw any conclusions from the antics of this particular West, I will go with the a priori odds - West has four non-ace spades and East two, so I will play West for the queen. But whoever mocked you for setting this problem had a point: it does not make a whole lot of sense to ask how one would play a hand when the opponents have clearly acted irrationally at almost every turn.

Not sure about all this. Why has West led dummy's suit? I'm going to draw trumps ending in hand and play a second heart. If West follows, I will finesse the jack. If not, I will play East for the singleton ace of spades.

Not really. You see, with most eight counts with four clubs to a single honour, partner would have doubled or would have raised hearts (especially if he could double with 3=2=4=4 shape, not being benighted). One of the reasons mathematicians cannot count is that they are unable to conceive of, or ascribe a meaning to, an indefinite article such as "a"; they persist in regarding it as denoting "one". Wherefore they lose all sense of what is "reasonably likely", and...

I mean that I thought South might not re-open - after all, several very strong players here have not done so, and I am not sure that I would have done so at the table. Having said that, your hand is so bad that there is almost no chance that partner does not have a penalty double - what else can he have, given that the opponents have advanced only as far as 2♣? Unless, of course, partner belongs to that group of benighted souls who cannot make a negative double without four spades, in which case there is little hope for him or for you. When the Iceman passed in Yokohama, I am sure he thought it was the correct call, and that his partner ought to have bid 3NT over 3♣ and not hoped for a reopening double. The position has, I have no doubt, been discussed among Iceland's top players (at least two of whom were among our opponents in this match) and I am sure they have concluded, as Frances has and as Gromoeller had in the match against Italy, that if you're going to open this, you're committed to reopening it or seeing it through in some other way.

I don't mind passing 1♥ - if I didn't, I would bid 1♠ and then I would not have any of these problems. Now, though, I'd better bid 4♥. After all, if partner can't make that when I put down the ace of spades and the queen of clubs... well, what did he want from my life?

At the other table, Gromoeller for Bamberger Reiter opened 1♥ and heard double, redouble, 1♠. He doubled for penalty, and the vugraph audience was treated to the rare sight of Lauria going for 800. The full deal was: [hv=d=s&v=e&n=sa3ha10dk1074cqj752&w=sj97h98daq6cak1093&e=s10852h7652dj982c8&s=skq64hkqj43d53c64]399|300|Scoring: IMP[/hv] We played this deal against Iceland. I was sitting out, and when I saw the auction proceed 1♥-2♣-pass-pass, I thought South would do well to reopen. Then I remembered a deal from the world championships in Yokohama, 1991, where an Iceman sitting South had a sub-minimum opening bid with two small clubs. He opened, and when 3C came back to him he passed and collected 300 in lieu of a vulnerable game. I have not the least doubt that the Icelanders vowed that this would never happen to them again.

Would chance 4NT planning, if partner shows an ace, to ask for the trump queen and risk the club position in seven spades. The problem is that one cannot also ask for third-round club control if, after a one-ace reply and a queen ask, partner is supposed to bid six spades with the trump queen and no side king. No doubt I will discover that I wrote the commentary for this simultaneous pairs, and excoriated anyone who got higher than four spades. Oh, well.

In actual play, West had the ace of hearts and a small singleton in diamonds. To make six clubs, one had to follow the line given by Tyler: king of spades, draw trumps, overtake the queen of spades and lead the king of hearts, discarding a diamond. Whether I would have found this line in six, I don't know. Since I was actually in seven, I was pleased to observe that the opening lead had been the ace of hearts, and I followed the advice given in the thread title.

Not sure where to put this, really, but I thought it might make a good intermediate-level test. [hv=d=s&v=n&n=saj2hkqj984dqjc83&s=skqhda7643cakqj102]133|200|Scoring: IMP[/hv] You, South, play in 6♣ after an uncontested auction. West leads a spade. If you elect at any point to draw trumps, East will turn up with ♣975 and West with ♣64. Plan the play.

No, it's not. Although West, if he has the queen of diamonds and understands declarer's problem, should play that queen as fast as he can from queen third, or even fourth, in practice he will not. Wherefore the Master wrote: We don't need too much birdlore, do we, To tell a flamingo from a towhee? Yet I cannot, and never will, Unless the silly birds stand still. He concluded, perhaps having been swindled by a West who stuck in DQ from Qxx, that I sometimes visualize in my gin The Audubon that I audubin.

I believe you, young Andy. It's the thousands who wouldn't that you have to convince.

Put more simply, no line will work if West has four or more clubs. Lawrence's line will work if West has three clubs; Trinidad's line will work if West has 0, 1 or 2 clubs. The a priori chance that West has exactly three clubs is about 36%. The a priori chance that he has more than three clubs is therefore about 32% (half of the 64% chance that he doesn't have exactly three). But when West has three spades and East none, the chance that East has more clubs than West increases by... well, by an amount that would seem significant even if you didn't know what it was. The vast array of figures in the posts above are no doubt designed to contradict my assertion that mathematicians cannot count. They still can't, but ever since the proof of the four-colour theorem, they have had to pretend that they believe computers can. Now, suppose that West had played the queen of diamonds [a] under the king or when you led the second round. How would, or should, you play then?

Don't mind opening one. As to those who would open six, my view was well expressed (in a different context) by Bobby Wolff, who said "I admire them - I just don't want their results."

More data required. What could I have bid over 1NT? More importantly, what would partner's double of 2D have meant? It's not that I would actually double - I would not, preferring 2S at the form of scoring and the vulnerability. But double could barely work in more than one way - if partner passes, that's good because we'll beat them 200 or more; if he has a fair hand with short spades and nine cards in the minors, that's also good because we might play a better partial than we would if I had bid 2S. All of which means that double is not totally sick. But 4 is not enough. Put me down for 4.8.

I believe that 5C expresses the opinion that, all in all, the best I can do to maximise our side's chances of obtaining a good result on the current deal is to offer to take eleven tricks with clubs as trumps. After all, that is what the majority of 5C bids mean without prior agreement to the contrary. Partner may have a contrary view that he is at liberty to express - as Frances says, if he believes that if I think I can take eleven tricks, I can in fact take twelve or thirteen, he may act accordingly. Other views are possible, and every partnership aiming at expert status should consider them. For example, it is generally thought that if partner opens 4S, it is more useful on grounds of frequency to play 5C as a slam try in spades, not a game try in clubs. Does this apply when partner has overcalled 4D with 4S? Here the "grounds of frequency" argument is unlikely to be of much value, since such sequences are not very frequent at all. But a good partnership might at least have the basic agreement that all undiscussed bids are natural if they can be natural. That way, at least it will be clear to the West on the actual hand that he ought to try 5S if anything, and not 5C. Of course, if North opens 3H, East bids 4D, South passes and West bids 4NT, that can be natural. Should it be? Maybe 4H should be Blackwood... These facts should all be noted down And ruminated on By every boy in Oxford town Who wants to be a Don.

[hv=d=n&v=b&n=s8654hak653d3cj96&w=saqj7hj7da97654ca&e=sk92hqdkq2ck87542&s=s103h109842dj108cq103]399|300|Scoring: IMP[/hv] East-West are a partnership whose experience is confined to the 80 boards they have so far played together in this tournament (I was West, Justin Hackett was East, Jason Hackett was in bed with the flu). There doesn't seem to be a facility for showing auctions here, so you will have to make do with the following narrative. North passed and East opened 1♣ (four-card majors, strong no trump, weak hands will open 1M if balanced and may open 1M with a longer minor). South passed and West bid 1♦ (not Walsh - no guarantee of game-forcing values if a major is held). North bid 1♥ and East doubled (exactly three diamonds, no other information vouchsafed). South bid 2♥, West bid 2♠, North passed and East bid 3♦ (minimum). South passed and West bid 3♥ (stopper-asking). North passed and East bid 4♣ (natural). South passed, and West bid 5♦, which ended the auction. Now, Justin and I are not a regular partnership, but these questions occurred to me: (1) At what point if any had this auction become forcing to game? For example, would East-West be allowed to bid: [hv=d=n&v=b&w=saqj7hj7da97654cq&e=sk92hq3dk82ckj754]266|100|Scoring: MP[/hv] like this: ...Pass-1♣-Pass 1♦-1♥-Double-2♥ 2♠-Pass-3♦-Pass 3♥-Pass-4♣-Pass 4♦-All pass Not that we'd necessarily make it if we did, but it would be the best we could do. (2) If West had "raised" 4♣ to 5♣ in the given auction, would this clearly be a control bid, begging for a heart control? Or can East-West play in 5♣? It seemed to me that at no point had East-West actually asserted that they had more than a 4-3 diamond fit, while they might have a pretty good club fit (West cannot bid a forcing 3♣ over 2♥ - or can he?) (3) Once East denied a heart stopper, it never entered my head that he might have a heart singleton. Can it be that we should not bid as much as we think we should bid, just because it's against the Law not to? For amusement only: at the other table North passed and East opened 1♣. South, Artur "The Great" Malinowksi, overcalled 1♦, a psyche. West bid 1♠, North passed, East bid 2♣ and West bid 3NT. North led... a low heart.